Portfolio Optimization with Mental Accounts

3 We integrate appealing features of Markowitz’s mean-variance portfolio theory (MVT) 4 and Shefrin and Statman’s behavioral portfolio theory (BPT) into a new mental accounting 5 (MA) framework. Features of the MA framework include an MA structure of portfolios, 6 a definition of risk as the probability of failing to reach the threshold level in each mental 7 account, and attitudes toward risk that vary by account. We demonstrate a mathematical 8 equivalence between MVT, MA, and risk management using value at risk (VaR). The ag9 gregate allocation across MA subportfolios is mean-variance efficient with short selling. 10 Short-selling constraints on mental accounts impose very minor reductions in certainty 11 equivalents, only if binding for the aggregate portfolio, offsetting utility losses from er12 rors in specifying risk-aversion coefficients in MVT applications. These generalizations of 13 MVT and BPT via a unified MA framework result in a fruitful connection between investor 14 consumption goals and portfolio production. 15